If you had one bad leg (fine for walking, not agile/strong enough to run on) how could you compensate for it in a fist fight?

Actually, this one’s pretty simple: Depending on the injury, you wouldn’t be able to get into lower stances, which is a distinct disadvantage. A lower center of gravity is harder to knock over, and has an advantage for power generation.

Also, it would impair your ability to kick. In my case, I can’t really drill in traditional kicks, because my knee will start to go after about 10 minutes. I can execute them, and I’ve been trained in a few, but my technique is permanently sloppy, because I don’t have the option to drill it until I have the technique down.